Which of the following numbers is a factor of 90? ${4,8,10,12,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $90$ by each of our answer choices. $90 \div 4 = 22\text{ R }2$ $90 \div 8 = 11\text{ R }2$ $90 \div 10 = 9$ $90 \div 12 = 7\text{ R }6$ $90 \div 14 = 6\text{ R }6$ The only answer choice that divides into $90$ with no remainder is $10$ $ 9$ $10$ $90$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $90$ $90 = 2\times3\times3\times5 10 = 2\times5$ Therefore the only factor of $90$ out of our choices is $10$. We can say that $90$ is divisible by $10$.